Question

In the figure, the centre of the circle is O and ∠STP = 40°.

1. m (arc SP) = ? By which theorem?
2. m ∠SOP = ? Give reason.

Answer 1

Given: ∠STP = 40°

i. m(arc SP) = 2∠STP 

⇒ m(arc SP) = 2 × 40° = 80°

Hence, m(arc SP) is 80° by inscribed angle theorem.

ii. m∠SOP = 2 × m∠STP

= 2 × 40° = 80°

As a result, m∠SOP is 80° since the angle subtended by an arc at the centre of the circle is twice the angle subtended by the arc at any point on the circle.